'''
A string of '0's and '1's is monotone increasing if it consists of some number of '0's (possibly 0), followed by some number of '1's (also possibly 0.)

We are given a string S of '0's and '1's, and we may flip any '0' to a '1' or a '1' to a '0'.

Return the minimum number of flips to make S monotone increasing.



Example 1:

Input: "00110"
Output: 1
Explanation: We flip the last digit to get 00111.
Example 2:

Input: "010110"
Output: 2
Explanation: We flip to get 011111, or alternatively 000111.
Example 3:

Input: "00011000"
Output: 2
Explanation: We flip to get 00000000.


Note:

1 <= S.length <= 20000
S only consists of '0' and '1' characters.
'''

class Solution(object):
    def minFlipsMonoIncr(self, S):
        """
        :type S: str
        :rtype: int
        """
        ones = [0]
        for char in S:
            ones.append(ones[-1] + int(char))
        # print ones
        result = float('inf')
        for index in range(len(ones)):
            zeroes = len(S) - index - (ones[-1]-ones[index])
            result = min(zeroes+ones[index], result)
        return result
